It has been interesting to read the discussion back and forth following my post. I do not have a degree in anything and failed abysmally at high school pure mathematics (applied mathematics I was good at as I could see a real-world use for what I was trying to learn) so my approach to the problem was purely empirical. I can't even qualify as an amateur mathematician as attempts to read the literature tell me that I don't understand the language being employed, I just hear a whoosh as it goes over my head.

However, I did very much enjoy writing the code and playing around with ideas so I'm grateful to tobyink for starting the thread!